A351448 Odd numbers k for which A003958(sigma(k)) = 2*A003958(k), where A003958 is multiplicative with a(p^e) = (p-1)^e and sigma is the sum of divisors function.

8181, 400869, 1507005, 3918213, 11151837, 22002273, 26669007, 47319957, 58170393, 73843245, 75825981, 83488077, 94338513, 108277641, 119656197, 126889821, 137740257, 163057941, 184758813, 191992437, 199226061, 202842873, 204768225, 220926933, 228160557, 258457473, 264328677, 277602471, 300496797

Offset

1,1

Comments

Odd numbers k such that A351442(k) = 2*A003958(k).

Any hypothetical odd term of A005820, if such a term exists, should appear in this sequence, in A347391, and in A016754 (odd squares).

None of the first 33 terms is a square, and all of them except 75825981 and 204768225 are multiples of 81. Note that 81 is one of the terms of A008848 (and of A231484), squares whose sum of divisors is also square (with A000203(81) = 121).

Links

Table of n, a(n) for n=1..29.

Index entries for sequences related to sigma(n)

Prog

(PARI)
A003958(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1]--); factorback(f); };
isA351448(n) = (n%2 && (A003958(sigma(n)) == 2*A003958(n)));

Crossrefs

Odd terms in A351447.

Cf. A000203, A003958, A005820, A008848, A016754, A231484, A339905, A347391, A351442.

Sequence in context: A205092 A014885 A252217 * A235095 A283954 A250939

Adjacent sequences: A351445 A351446 A351447 * A351449 A351450 A351451

Keyword

nonn

Author

Antti Karttunen, Feb 12 2022

Status

approved