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A123373 a(n) = Sum_{i=1..n} (Sum_{j=1..n} prime(i)^prime(j)). 2
4, 48, 3598, 924780, 287358579128, 339575512147572, 836406636653653232322, 2225332017808171682043720, 21158384827910606570843063431876, 2570789828135881020104992992114519012237948 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

p divides a(p-1) for prime p = {2, 3, 5, 23, 29, ...}.

All terms are even.

2^2 divides a(n) for n = {1, 2, 4, 5, 6, 8, 9, 10, 12, 13, 14, 16, 17, 18, 21, 25, 26, 29, 30, 33, 37, 41, 45, 48, 49, 50, 52, ...}.

2^3 divides a(n) for n = {2, 5, 8, 12, 13, 16, 18, 21, 29, 37, 45, 48, 50, 52, 53, 58, 61, 64, 69, 76, 77, 85, 88, 93, 94, 98, ...}.

2^4 divides a(n) for n = {2, 12, 13, 18, 29, 45, 53, 58, 64, 76, 77, 93, 102, 109, 112, 125, 128, 133, 141, 149, 150, 157, 170, ...}.

2^5 divides a(n) for n = {12, 13, 18, 53, 58, 64, 77, 93, 102, 112, 141, 149, 150, 173, 178, 188, 190, 196, 205, 232, 234, 237, ...}.

2^6 divides a(n) for n = {13, 58, 64, 102, 150, 173, 178, 190, 205, 232, 234, 237, 245, 277, 285, 290, 325, 333, 382, 429, 434, ...}.

2^7 divides a(n) for n = {13, 58, 64, 150, 173, 178, 205, 234, 325, 382, 472, 573, 592, 596, 621, 628, 653, 757, 796, 893, 950, ...}.

2^8 divides a(n) for n = {13, 58, 64, 178, 205, 325, 382, 573, 653, 757, ...}.

2^9 divides a(n) for n = {13, 58, 64, 178, 325, 382, 653, 757, ...}.

2^10 divides a(n) for n = {64, 178, ...}.

2^11 divides a(n) for n = {64, 178, ...}.

2^12 divides a(n) for n = {178, ...}.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..76

MATHEMATICA

Table[Sum[Sum[Prime[i]^Prime[j], {i, 1, n}], {j, 1, n}], {n, 1, 13}]

PROG

(PARI) for(n=1, 10, print1(sum(j=1, n, sum(k=1, n, (prime(k))^(prime(j)))), ", ")) \\ G. C. Greubel, Oct 25 2017

(Python)

from sympy import prime

def A123373(n): return sum(prime(i)**prime(j) for i in range(1, n+1) for j in range(1, n+1)) # Chai Wah Wu, Jan 08 2022

CROSSREFS

Cf. A086787 (Sum_{i=1..n} (Sum_{j=1..n} i^j)), A122004.

Sequence in context: A112693 A239162 A136384 * A264265 A132510 A058311

Adjacent sequences:  A123370 A123371 A123372 * A123374 A123375 A123376

KEYWORD

nonn

AUTHOR

Alexander Adamchuk, Oct 12 2006

STATUS

approved

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Last modified August 17 23:13 EDT 2022. Contains 356204 sequences. (Running on oeis4.)