A388279 Positions of powerful terms among the numbers satisfying Euler's condition for odd perfect numbers (A228058).

520, 2388, 3765, 5388, 7295, 11813, 14437, 17313, 20410, 27274, 31043, 35032, 38585, 39232, 48315, 53225, 58264, 63548, 74678, 80615, 86709, 92980, 97840, 106224, 113158, 120225, 127565, 131066, 142765, 150678, 158778, 167069, 175553, 181164, 184223, 193073, 202091, 211325, 230418, 240210, 250337, 260405, 281441

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..811

Formula

For all n >= 1, A228058(a(n)) = A386428(n).

Example

A386428(2) = 153125 = 5^5 * 7^2 occurs as the 2388th term of A228058, therefore a(2) = 2388.

Prog

(PARI)
is_A228058(n) = if(!(n%2)||(omega(n)<2), 0, my(f=factor(n), y=0); for(i=1, #f~, if(1==(f[i, 2]%4), if((1==y)||(1!=(f[i, 1]%4)), return(0), y=1), if(f[i, 2]%2, return(0)))); (y));
i=0; forstep(n=1, 1+(2^33), 4, if(is_A228058(n), i++; if(ispowerful(n), print1(i, ", "))));

Crossrefs

Cf. A001694, A228058, A386428.

Sequence in context: A147854 A147856 A389169 * A094903 A250693 A200427

Adjacent sequences: A388276 A388277 A388278 * A388280 A388281 A388282

Keyword

nonn

Author

Antti Karttunen, Sep 28 2025

Status

approved