A387160 Terms of the form prime * m^2 in A351554.

2, 3, 7, 20, 27, 28, 31, 127, 496, 567, 775, 2268, 3100, 8128, 8191, 27783, 131071, 403172, 524287, 3628548, 17389708, 32656932, 33550336, 127926848, 1087307452, 1248461136, 1408566348, 2147483647, 7802882100, 8589869056, 9785767068, 10362074688, 31211528400, 88071903612

Offset

1,1

Comments

Conjecture: This sequence has no common terms with A228058. See comments in A386430.

Links

Table of n, a(n) for n=1..34.

Index entries for sequences where odd perfect numbers must occur, if they exist at all

Index entries for sequences computed from indices in prime factorization

Index entries for sequences related to sigma(n)

Formula

{k | A162642(k) = 1 and A351555(k) = 0}.

Prog

(PARI)
A003961(n) = { my(f = factor(n)); for(i=1, #f~, f[i, 1] = nextprime(f[i, 1]+1)); factorback(f); };
A351555(n) = { my(s=sigma(n), f=factor(s), u=A003961(n)); sum(k=1, #f~, if((f[k, 1]%2) && 0!=(u%f[k, 1]), (valuation(n, f[k, 1])!=f[k, 2]), 0)); };
isA387160(n) = (isprime(core(n)) && (0==A351555(n)));

Crossrefs

Intersection of A229125 and A351554.

Cf. A162642, A228058, A351555, A386430.

Subsequences: A000396\{6}, A000668.

Sequence in context: A244917 A172976 A171655 * A293683 A006073 A052402

Adjacent sequences: A387157 A387158 A387159 * A387161 A387162 A387163

Keyword

nonn

Author

Antti Karttunen, Aug 24 2025

Extensions

Terms a(29)-a(34) from Giovanni Resta, Aug 25 2025

Status

approved